Kim and Opfer (2017) found that number-line estimates increased approximately logarithmically with number when an upper bound (e.g., 100 or 1000) was explicitly marked (bounded condition) and when no upper bound was marked (unbounded condition). Using procedural suggestions from Cohen and Ray (2020), we examined whether this logarithmicity might…

Young children's estimates of numerical magnitude increase approximately logarithmically with actual magnitude. The conventional interpretation of this finding is that children's estimates reflect an innate logarithmic encoding of number. A recent set of findings, however, suggests that logarithmic number-line estimates emerge via a dynamic…

There is an ongoing debate over the psychophysical functions that best fit human data from numerical estimation tasks. To test whether one psychophysical function could account for data across diverse tasks, we examined 40 kindergartners, 38 first graders, 40 second graders and 40 adults' estimates using two fully crossed 2 × 2 designs, crossing…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

We investigated the relation between children's numerical-magnitude representations and their memory for numbers. Results of three experiments indicated that the more linear children's magnitude representations were, the more closely their memory of the numbers approximated the numbers presented. This relation was present for preschoolers and…